Question

A fund must be prepared so that a new baby
born will have money of 50 million rupiah per year, for 4
years, when he was 18 years old. The grandfather of the paternal family decided
will finance the first two 50 million rupiah payments, meanwhile
grandfather from the maternal family will fund the third and third payment
pat. How big is the difference in investment required by grandfather
from the father and the grandfather of the mother (at time 0), if both invest-
tation at an annual effective rate of 4%?

Answer 1

Assuming payments in advance (first payment at t=18) and so on.

1   Investment by paternal grandparents:

Investment needed at t=0 is the PV of payments in years 18 and 19

Given, each payment is 50 million and interest rate is 4% (annual)

Investments needed now= 50*PVIF (4%, 18) + 50*PVIF(4%,19)

=50*0.4946 + 50*0.4746

=24.73+23.73= 48.46 million rupiah

2   Investment by maternal grandparents:

Investment needed at t=0 is the PV of payments in years 20 and 21

Given, each payment is 50 million and interest rate is 4% (annual)

Investments needed now= 50*PVIF (4%, 20) + 50*PVIF(4%,21)

=50* 0.4564+ 50*0.4388

=22.82+21.94= 44.76 million rupiah

Difference in amount needed= 48.46-44.76 = 3.70 million rupiah